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Modular Arithmetic

  1. Jul 11, 2008 #1
    1. The problem statement, all variables and given/known data

    Show that if a = (b mod m) and c = d(mod m) and m => 2, then a - c = (b - d)(mod m)

    2. Relevant equations

    c = d(mod m) <=> m|(c - d)
    d = c + xm

    3. The attempt at a solution

    I don't know how any equivalences for a = (b mod m), is there a way to get b from a = (b mod m)?

    I had a + c = (b mod m) + d(mod m) but I'm not sure where to go from there
  2. jcsd
  3. Jul 11, 2008 #2


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    a= b (mod m) means that a- b is divisible by m or that a- b= mp for some integer p.
    Similarly, c= d (mod m) means that c- d= mq for some integer q.

    Now what does a-c= b- d (mod m) mean?
  4. Jul 11, 2008 #3
    a - c = (b - d)(mod m) would be (a - c) - (b - d) = mx for some x

    But its a = (b mod m)
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